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If you have no need to use MSOffice for file compatibility. Which is best Open Office or LibreOffice?

LibreOffice is better, more current, and has more features. It is a fork of Open Office after Oracle abandoned development of Open Office. You can read about it here.

If you don't have really advanced needs in an office suite LibreOffice will work just fine.
 
There are many alternatives, such as iWork, NeoOffice, LibreOffice, OpenOffice, Google Docs, etc. Searching the forum will reveal dozens of threads discussing these various alternatives and the pros and cons of each, although I don't see LibreOffice mentioned as often as others.

LibreOffice isn't mentioned as much as it is the relative newcomer.

I read nothing but praise for LibreOffice when compared to other free alternatives. I use it as my main suite and have had no issues so far
 
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